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3) What is wrong with the following proof that all horses have the same color? Let...

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3) What is wrong with the following proof that all horses have the same color? Let P(n) be the proposition that all the horse

3) What is wrong with the following proof that all horses have the same color? Let P(n) be the proposition that all the horses in a set of n horses are the same color. Clearly, P(1) is true. Now assume that P(n) is true. That is, assume that all the horses in any set of n horses are the same color Consider any n1 horses; number these as horses 1,2,3,...,n,n +1. Now the first n of these horses all must have the same color, and the last n of these must also have the same color. Since the set of the first n horses and the set of the last n horses overlap, all n 1 must be the same color This shows that P(n+ 1) is true and finishes the proof by induction.

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